Carving toboggan

ABSTRACT

There is disclosed a vehicle ( 1 ) for travelling over snow or the like and comprising a straight runner means ( 19 ) and one or more curved runners ( 21, 23, 25 ) convex towards the straight runner means. When the vehicle is level it travels on the straight runner means in a straight line. By rolling the vehicle to one side, one of the curved runners engages the snow and the vehicle performs a carving turn whose radius is determined by the radius of the runner. Different turn radii are selectable by altering the roll angle of the vehicle. Embodiments are described for use on snow and ice and a wheeled version for use on hard surfaces is also disclosed.

[0001] This invention relates to ice skates and toboggans, and more particularly but not exclusively, to a class of boards (also known as snowdecks) for use primarily on snow. In this context, a snowdeck may be regarded as a type of skateboard for use on snow, or as a binding-less snowboard.

[0002] Conventional toboggans are well known but suffer from the disadvantage that they cannot readily be steered. A rider can produce some form of steering by, for example, sticking out his foot to brake one side of the toboggan but this form of steering falls far short of what is possible using skis or a snowboard. Skis allow a skier to steer but skis suffer from the disadvantage that it is difficult for a beginner to use them effectively. Snowboards also allow their riders to steer themselves but, like skis, are difficult for a beginner to use effectively. On the other hand, toboggans are very easy to use but do not offer the turning ability of skis or snowboards.

[0003] Skis and snowboards allow effective turns to be made as they can be made to carve through the snow. By carve, it is meant that the ski or snowboard is deformed by the user so that the footprint in the snow of the ski or snowboard is formed into an arc. As the front portion of the ski or snowboard travels over the snow, it forms a groove in the snow and the rear portion of the ski or snowboard subsequently travels through that groove. If the footprint does not have the appropriate arcuate shape for the turn being performed, or if the footprint has some shape other than arcuate, then the rear portion will not be able to travel through the groove. In this situation the rear portion will modify the shape of the groove, thereby increasing friction between the ski or snowboard and the snow. In extreme cases, the rear portion will barely follow the groove, and will instead skid across the snow.

[0004] An important factor in the use of skis and snowboards is dynamic stability. To initiate a turn at a given speed, a rider momentarily unbalances himself so that he leans over to one side. As he leans over, he also tilts and flexes the ski or snowboard so that its footprint in the snow is bent into an arc. The arc shape causes the rider to follow a circular path and the centrifugal force produced as a result of the circular path is balanced by the lean of the rider. The rider is therefore dynamically stable: even though he is leaning over to one side, he does not fall over. He can continue to lean over to one side indefinitely provided that he continues to follow the appropriate circular path over the snow at the appropriate speed.

[0005] The need to instinctively bend the footprint of the ski or snowboard into the appropriate shape, and to balance the resultant dynamic forces without falling over, are factors that make skiing and snowboarding difficult.

[0006] There is therefore a need for an apparatus that allows carving turns to be readily made in snow.

[0007] Skateboarding has become a popular pastime and apparatuses have been devised in an attempt to recreate the skateboarding experience on snow and thus allow skateboarding enthusiasts to enjoy their pastime as a winter sport. Such devices do not emulate the turning ability of a skateboard and there is therefore a need for an apparatus which will allow effective turning on snow.

[0008] FR 2383679 discloses an apparatus, for use on snow, having an underside which is curved both longitudinally and transversely. Longitudinal guides mounted on the underside of the apparatus are curved so that guides nearer the longitudinal axis are less curved than guides located further away from the longitudinal axis.

[0009] U.S. Pat. No. D448,441 discloses a snow-sliding apparatus having a flat underside and having straight longitudinal grooves.

[0010] According to one aspect of the invention, there is provided a vehicle for travelling over a carveable medium such as snow, sand or ice, and having a longitudinal axis about which the vehicle can roll relative to the surface of the medium. The vehicle comprises a straight runner means for travelling on the medium in a substantially straight line when the vehicle is tilted at a first predetermined roll angle relative to the medium and a first curved runner convex toward the straight runner means. The first curved runner comprises a substantially circularly arcuate portion of a first radius for travelling on the medium in a substantially circular path by carving the medium when the vehicle is tilted at a second predetermined roll angle relative to the medium.

[0011] Preferably, the straight runner means comprises a straight runner, but alternatively the straight runner means may comprise a pair of oppositely curved runners.

[0012] In a further alternative embodiment, the vehicle may comprise a second curved runner arranged on the side of the straight runner means opposite to the first curved runner and convex toward the straight runner means. The second curved runner may comprise a substantially circularly arcuate portion of a second radius for travelling on the medium in a substantially circular path by carving the medium when the vehicle is at a third predetermined roll angle relative to the medium.

[0013] In a yet further preferred embodiment, the first and second radii are equal and most preferably, the first and second curved runners are symmetrical with respect to the straight runner means.

[0014] The vehicle may comprise a plurality of curved runners arranged on one side or both sides of the straight runner means.

[0015] An advantage of such an vehicle is that by tilting or rolling the vehicle, a rider can select an appropriate carving surface to perform a turn of a desired radius.

[0016] Another advantage of the vehicle is that the angle of tilt or roll required to select a carving surface corresponds with the curvature of the selected carving surface, so that a rider more easily achieves the dynamic balancing required to execute good carving turns. The correspondence between the angle of tilt and the curvature is the same as the correspondence between the angle of lean of a bicyclist and the curvature of the path that the bicyclist follows. Many people are familiar with riding a bicycle and thus the vehicle allows such people to readily become proficient at performing carving turns on snow.

[0017] In one embodiment the vehicle has a form similar to that of a skateboard. In other embodiments the apparatus may be used as a toboggan or as ice skates.

[0018] Preferred embodiments of the present invention will now be described by way of examples and with reference to the following drawings, in which:

[0019]FIG. 1 is a perspective view of a snowdeck according to the present invention being ridden by a rider;

[0020]FIG. 2 is a perspective view of the underside of the snowdeck;

[0021]FIG. 3 is a plan view of the underside of the snowdeck;

[0022]FIG. 4 is an end elevation view of the snowdeck;

[0023]FIG. 5 is a side elevation view of the snowdeck;

[0024]FIG. 6 shows a cross-sectional view of the snowdeck in a plane located towards one end of the snowdeck;

[0025]FIG. 7 shows a cross-sectional view of the snowdeck at a plane located at the centre of the snowdeck;

[0026]FIG. 8 shows a partly perspective view, not to the correct proportions, which illustrates the geometry of the carving surfaces of the snowdeck;

[0027]FIG. 9a shows the rider and a cross-sectional view of the snowdeck and also shows a plan view of the rider and snowdeck together with the track made in the snow by the snowdeck;

[0028]FIG. 9b shows the rider and a cross-sectional view of the snowdeck with the snowdeck tilted by a small angle, and also shows the curved track made in the snow by the snowdeck due to the small tilt;

[0029]FIG. 9c shows the rider and a cross-sectional view of the snowdeck with the snowdeck tilted by a medium angle, and also shows the curved track made in the snow by the snowdeck due to the medium tilt;

[0030]FIG. 9d shows the rider and a cross-sectional view of the snowdeck with the snowdeck tilted by a large angle, and also shows the curved track made in the snow by the snowdeck due to the large tilt;

[0031]FIG. 10a shows a snowdeck and rider following an ‘S’-shaped path comprising a left turn, a straight section followed by a right turn;

[0032]FIG. 10b shows a detailed view of the track made in the snow by a snowdeck following the path shown in FIG. 10a;

[0033]FIG. 11 shows a hull which may be attached to a skateboard to form a snowdeck;

[0034]FIG. 12a shows a perspective view of a carving toboggan according to the present invention;

[0035]FIG. 12b shows a perspective view of a rider standing on the carving toboggan and secured to the carving toboggan by foot straps; and

[0036]FIG. 13 shows a perspective view of an ice skating boot according to the present invention.

[0037]FIG. 1 shows a snowdeck 1 being ridden down a slope by a rider 3 over snow 5 and also shows the track 7 made in the snow by the snowdeck 1. In this embodiment the snowdeck 1 comprises a polyethylene hull 9 which engages the snow. Mounted on top of the hull 9 is a plywood deck 11 which supports the rider 3. In this embodiment the snowdeck 1 is 81.3 cm long (32 inches), 20.3 cm wide (8 inches) and has a height of 7 cm (2¾ inches) at the centre of the snowdeck 1. In this embodiment four bolts 14 are used at each of two securing regions 13 to secure the deck 11 to the hull 9. In this embodiment the top surface of the deck 11 is covered with foam rubber to increase the grip and so reduce the risk of the rider 3 becoming dismounted. Also, in this embodiment, an attachment point 2 is provided so that a tether 4 can be used to secure the snowdeck 1 to the ankle (for example) of the rider 3. The tether 4 may be used on public pistes to prevent the snowdeck 1 from travelling down the piste without the rider 3.

[0038] The rider 3 can steer the snowdeck 1 by leaning himself and the snowdeck 1 over to one side; the greater the lean, the sharper the turn. This is explained in more detail in relation to FIGS. 9 and 10.

[0039]FIGS. 2, 3, 4 and 5 show a perspective view of the underside of the snowdeck 1, a plan view of the underside, an end elevation view of the snowdeck 1 and a side elevation view, respectively. As can be seen, the snowdeck 1 has a vertical plane of symmetry about which the two sides of the snowdeck 1 are symmetric, and has a longitudinal axis 15 in that plane. The snowdeck 1 also has a vertical plane of symmetry about which the two ends of the snowdeck 1 are symmetric, and has a transverse axis 17 in that plane.

[0040] The snowdeck 1 has a straight central surface 19 which bears the majority of the weight of the rider 3 when the snowdeck 1 is being ridden in a straight line. Three convex carving faces 21, 23, 25 are provided on each side of the snowdeck 1 and face toward the centreline of the snowdeck to allow the rider 3 to make carving turns in the snow 5 by tilting the snowdeck 1 in order to select one of the carving faces 21, 23, 25. The profile of the straight surface 19 and of the carving faces 21, 23, 25 is described in more detail in relation to FIGS. 6 to 8.

[0041] The hull 9 has a canoe-like shape. As can be seen most clearly from FIG. 5 in conjunction with FIG. 2, each of the end regions 27 of the hull 9 is rounded off and tapered upwards to form an angle of a relative to the horizontal. In this embodiment a has a value of about 38°. More generally, a is preferably in the range 30° to 45°. The end regions 27 allow the hull 9 to slide over relatively small irregularities in the snow 5, for example furrows, without digging into such irregularities. Another advantage provided by the end regions 27 is that they allow a rider 3 who is sufficiently skilled to perform “trick” manoeuvres on the snowdeck 1 which are analogous to those which may be performed on a skateboard. Such tricks typically involve pushing down on one end of the deck 11 so that the other end of the deck 11 is raised upwards, or even so that the entire snowdeck 1 is bounced up from the snow 5. If the straight surface 19 and the carving faces 21, 23, 25 extended as far as the end regions 27 then it would be more difficult to perform such manoeuvres as the hull 9 would tend to cut into the snow 5 rather than riding over small irregularities in the surface of the snow 5.

[0042] An axis 37 is shown in FIG. 3 lying transverse to the hull 9 at the widest point of the hull 9 before the profile of the hull 9 changes because of the curvature of the end region 27. The longitudinal axis 15, the transverse axis 17 and the axis 37 are shown in FIGS. 3 to 5 as lying just below the straight surface 19.

[0043] Each of the carving faces 21, 23, 25 is provided with a respective running face 31, 33, 35 facing generally downwards as seen in FIGS. 4 and 5. The running faces 31, 33, 35 are curved and meet the lower edges of their respective carving faces 21, 23, 25 at substantially right angles. The running faces may meet their respective carving faces at other angles, but the angle must not be so acute as to weaken the edge, nor so obtuse as to reduce the carving effect of the edge. Angles from 75° to 105° are foreseen with angles between 85° and 95° being preferred. The angle may vary along the length of the snow deck. The running faces 31, 33, 35 are discussed in more detail in relation to FIGS. 6 to 8.

[0044] As can be seen most clearly from FIG. 2 in conjunction with FIG. 3, on each side of the snowdeck 1 there are three recess surfaces 41, 43, 45 which define, with carving faces 21, 23, 25 longitudinal grooves (in the hull 9). There are two recess surfaces 41, one on each side of the straight central surface 19. Each recess surface 41 connects one edge of the straight surface 19 to the upper edge of the respective carving face 21. Similarly, each of the two recess surfaces 43 connects the outer edge of a respective running face 31 to the upper edge of the next outer carving face 23, and similarly the two recess surfaces 45 connect the outer edges of the running faces 33 to the upper edges of the carving face 25. The sides of the hull 9 form side faces 47.

[0045]FIGS. 6 and 7 show the configuration of the carving faces 21, 23, 25, the running faces 31, 33, 35 and the recess faces 41, 43, 45 in more detail. FIG. 6 shows a cross-sectional view of the snowdeck 1 in the plane XX′ of FIG. 3. The plane XX′ is the widest part of the hull 9 before the profile of the hull 9 changes because of the upward curvature of the end region 27. FIG. 7 shows a cross-sectional view of the snow deck 1 in the plane YY′ of FIG. 3. The plane YY′ is at the narrowest part of the hull 9 and includes the transverse axis 17.

[0046] As can be seen from FIG. 6, the underside of the hull 9 at this section has a generally arcuate transverse profile with a radius of rO_(x) and centre O_(x) on the longitudinal plane of symmetry of the snowdeck 1. In this embodiment rO_(x) is 18.5 cm. The axis 37 is tangential to the circle 51X defined by the radius rO_(x) at a point T_(x) beneath the centre of the straight surface 19. In the plane XX′, each of the two carving faces 21 lies along a part of one of the two radii 61 that are offset from vertical by an angle b. Similarly, each of the two carving faces 23 lies on part of one of the two radii 63 that are offset from vertical by an angle c, and each of the two carving faces 25 is a segment of one of the two radii 65 that are offset from vertical by an angle d. In this embodiment, the angles b, c and d are 11°, 18.4° and 30°, respectively.

[0047] Measured along their respective radii 61, 63, 65, the carving faces 21, 23, 25 have a “height” of 15 mm at this section of the hull 9.

[0048] The running faces 31, 33, 35 can be seen in FIG. 6 to lie tangentially to the circle 51X. In this embodiment, each of the running faces 31, 33, 35 has a width of 4 mm (the lengths of the running faces 31, 33, 35 correspond to that of their respective carving faces 21, 23, 25 along the hull 9).

[0049] Although the carving faces 21, 23, 25 lie along the radii 61, 63 and 65, respectively, in the plane XX′ the carving faces 21, 23, 25 are also all part-cylindrical surfaces. This can be seen from FIG. 7 which shows that the carving faces 21, 23, 25 bunch together as they approach the plane YY′ at the mid-length of the snow deck (at the transverse axis 17). The lines 71, 73, 75 (in the plane YY′) correspond to the radii 61, 63, 65, in the plane XX′ respectively, in that the carving faces 21, 23, 25 lie along parts of the lines 71, 73, 75. The lines 71, 73, 75 do not meet at a common point, but meet in pairs at different heights above the deck 11.

[0050]FIG. 7 also shows the respective radii r1, r2, r3 of the cylinders of whose surfaces the carving faces 21, 23, 25 are parts. The axes of these cylinders lie in the plane YY′ and are inclined to the plane of symmetry of the snowdeck by angles corresponding to angles b, c and d, respectively. In this embodiment r1 is 4.7 m, r2 is 1.9 m and r3 is 0.7 m. (Note that the radii r1, r2, r3 are not shown in FIG. 6 as that Figure is not in the plane YY′ of the cross-sectional view).

[0051]FIG. 8 provides an alternative way of appreciating that the carving faces 21, 23, 25 are parts of respective cylindrical surfaces. Note that in order to fit FIG. 8 satisfactorily on a page, the proportions of FIG. 8 are not to scale as the radius r3 is here shown as being smaller than the radius rO_(x); r3 is actually 3.8 times larger than rO_(x). FIG. 8 shows two cylinders 81, of radius r3, of which the carving faces 25 are parts and also shows the carving faces 25 without the remainder of the hull 9 or the deck 11.

[0052] As shown, the axes 83 of the two cylinders 81 are offset from vertical by the angle d, and the axes 83 lie in the same plane YY′ as the cross-sectional view of FIG. 7 (which contains the transverse axis 17). The two axes 83 intersect above the longitudinal axis 15 of the snowdeck 1 at point I which is higher above the deck 11 than O_(x) (and hence is also higher than O_(y) since O_(x) and O_(y) are the same height above the deck). The length, l, of the generators of each of the cylinders 81 is 15 mm and this is the height of the carving faces 25. As shown, the lowermost edges of the carving faces 25 lie on the circle 51X in the plane XX′.

[0053]FIG. 7 also shows that the running faces 31, 33, and especially the running face 35, protrude beyond the circle 51Y. This can be understood by reference to FIG. 8 which shows that the radii 65 of circle 51X and the lines 75 which are extensions of the generators of the cylindrical surface 25 in the plane YY′ lie in different planes, and that the radii 65 intersect at a point O_(x) which is higher above the deck 11 than the intersection point Z of the lines 75. The circle 51Y has the same radius, rO_(y), as that of the circle 51X and meets the transverse axis 17 tangentially at a point T_(y) beneath the centre of the straight surface 19. (T_(x) and T_(y) both lie on the longitudinal axis 15, as shown by FIG. 8). Thus, in effect, O_(x) and O_(y) define part of a cylinder which corresponds to the general cross sectional profile of the hull 9 in a plane transverse to the longitudinal axis 15. The end regions 27 are upwardly inclined from the ends of this cylinder.

[0054] As can be seen from FIG. 6, the hull 9 has a generally arcuate profile in transverse section near the end regions 27 but, as can be seen from FIG. 7, has a flatter transverse sectional profile near the middle of the hull 9. Arranging for the profile of the hull 9 to vary along the length of the hull 9 in this way provides several advantages.

[0055] Firstly, a rider 3 will typically use the snowdeck 1 so that his centre of gravity is located towards the centre of the snowdeck 1 so that the central surface 19 of the snowdeck 1 is parallel to the surface of the snow 5. With the centre of gravity of the rider 3 located towards the rear of the snowdeck 1, the rearmost portion of the hull 9 will bear the majority of the rider's weight and be urged into the snow 5 more than the middle or front portions, and this may assist the rider to move off from rest.

[0056] Secondly, the relatively flat profile towards the middle of the hull 9 minimises the extent to which the snowdeck 1 sinks into the snow 5 when stationary. This helps the rider 3 to move off from a standing start as the snowdeck 1 will not tend to sink too far into the snow 5. Once the snowdeck 1 is moving it will tend to plane over the snow 5.

[0057]FIG. 9a shows the rider 3 travelling along the Z axis without tilting the snowdeck 1, so that it runs on the straight surface 19 and travels along a straight line, forming a straight track 90 a in the snow 5. The instantaneous footprint 19′ of the straight surface 19 is also shown.

[0058]FIG. 9b shows the rider 3 travelling along a curved path, having tilted the snowdeck 1 at a small angle b so that the carving face 21 engages the snow 5. This causes the snowdeck 1 to travel along a curved path of radius r1, thereby forming a gently curved track 90 b in the snow 5. As shown, the carving face 21 is now vertical and does not bear any of the weight of the rider 3. The weight of the rider 3 is borne by the horizontal running face 31, together with the recess face 43. The instantaneous footprint 21′ of the carving face 21, running face 31 and recess face 43 is also shown.

[0059] Similarly, FIG. 9c shows the rider 3 travelling along a more tightly “curved” path having tilted the snowdeck 1 at a medium angle c so that the carving face 23 engages the snow 5 and causes the snowdeck 1 to travel along a curved path of radius r2, thereby forming a moderately curved track 90 c in the snow 5. As shown, the carving face 23 is now vertical and does not bear any of the weight of the rider 3. The weight of the rider 3 is borne by the now horizontal running face 33, together with the recess face 45. The instantaneous footprint 23′ of the carving face 23, running face 33 and recess face 45 is also shown.

[0060] Finally, FIG. 9d shows the rider 3 travelling along a tightly curved path having tilted the snowdeck 1 at a large angle d so that the carving face 25 engages the snow and causes the snowdeck 1 to travel along a curved path of radius r3, thereby forming a sharply curved track 90 d in the snow 5. AS shown, the carving face 25 is now vertical and does not bear any of the weight of the rider 3. The weight of the rider 3 is borne by the now horizontal running face 35, together with the side face 47 of the hull 9. The instantaneous footprint 25′ of the carving face 25, running face 35 and side face 47 is also shown.

[0061] The footprint 25′ is shown to be thinner and shorter than the footprint 19′, as is apparent from FIG. 3 which shows the straight surface 19 to be longer and wider than the carving face 25.

[0062]FIG. 10a shows the rider 3 riding the snowdeck 1 along an ‘S’ shaped path 100 comprising a left hand turn 101, followed by a straight section 102 and finally a right hand turn 103. The left hand turn becomes progressively shallower as the rider 3 approaches the straight section 102. The right hand turn 103 becomes progressively sharper as the rider 3 leaves the straight section 102 behind. The track that the snowdeck 1 makes in the snow 5 while following the path 100 is shown in more detail in FIG. 10b.

[0063] The initial part of the left hand turn 101 is made with the snowdeck tilted by a large angle d to the left so that it forms a sharply curved track 90 d in the snow. As the rider 3 reduces the tilt of the snowdeck to a medium angle c, his weight is progressively transferred from the carving face 25, running face 35 and side edge 47 to the carving face 23, running face 33 and recess face 45. As his weight is transferred, there is a period of time during which the carving face 25 and the carving face 23 are both engaged in the snow 5 and during this time tracks 90 d and 90 c, respectively, are formed simultaneously, as shown in FIG. 10b. Note that during this time neither of the carving faces 25 or 23 is vertical and thus neither face is truly “carving” the snow, so the friction between the snowdeck 1 and the snow 5 is increased.

[0064] Once the tilt of the snowdeck 1 has been reduced to the medium angle c, only the carving face 23 is vertical and only a single track is left in the snow 5. As the rider 3 continues to reduce the tilt of the snowdeck 1, the snowdeck 1 will gradually form a track 90 b as well as 90 c. With a further reduction of the tilt of the snowdeck 1 to the small angle b, only a track 90 b will be formed. As the tilt angle is then reduced to an angle smaller than b, further the straight surface 19 engages the snow and when the snow deck is horizontal only a straight track 90 a is formed in the snow 5.

[0065] As the rider 3 tilts the snowdeck 1 progressively to the right in order to make the right hand turn 103, the above sequence of transfers is reversed with the carving edges on the right-hand side of the board being sequentially engaged with the snow to make the tracks 90 b, 90 c and 90 d which are arcs of respective circles. These circles have been shown more clearly in the right hand turn 103 portion of FIG. 10b.

[0066] For simplicity, in the foregoing discussion for FIGS. 9 and 10 of the tracks made by the snowdeck 1, it was assumed that no more than two carving faces 21, 23, 25 ever simultaneously engage the snow 5. In fact, the number of carving faces that engage the snow depends on several factors such as the weight of the rider 3, the softness or powder quality of the snow 5 and also on the surface area of the underside of the hull 9. A heavy rider 3 will cause the hull 9 to sink lower into the snow 5, thus engaging more carving faces than a light rider 3. If the hull 9 is provided with a sufficiently large surface area, for example by widening or lengthening the running faces 31, 33, 35 or the straight surface 19, then the weight of the rider 3 will be distributed over a larger area, thus minimising the amount by which the hull sinks 9 into the snow 5.

[0067] The way in which the angles of tilt, b, c, d, of the various carving faces 21, 23, 25 of the snowdeck 1 are made to correspond with their respective radii r1, r2, r3 of curvature will now be discussed.

[0068] The angle of tilt of the carving faces 21, 23, 25 and the curvature of the carving faces 21, 23, 25 are chosen to be related, at predetermined velocities, by equation (1): $\begin{matrix} {{\tan \quad ({tilt})} = \frac{{velocity}^{2}}{{{radius}.{gravity}.\cos}\quad ({slope})}} & (1) \end{matrix}$

[0069] where gravity is 9.8 m/s² and where slope is the inclination of the piste.

[0070] To design a set of carving faces for the snowdeck 1, it is first necessary to have some idea of the velocity at which turning will be performed. This can easily be determined empirically by measuring the typical velocity of the snowdeck 1. As the profile of the hull 9 affects the typical velocity that a rider 3 will achieve, several iterations of the design process may sometimes be required. For the snowdeck 1, the carving faces 21, 23, 25 have been designed to work at 3 m/s, 2.5 m/s and 2 m/s, respectively. In practise, each carving face will work over a range of velocities.

[0071] An advantage of designing the inner carving faces to work at higher speeds and greater radii of turn than the outer carving faces is that the resultant snowdeck will, to some extent, compensate for tilting errors of the rider 3, thus making it even easier to use. If the rider 3 exceeds the velocity range for a particular carving edge then the centrifugal force acting on the rider 3 will tend to push the rider 3 so that he tilts the snowdeck 1 onto a more central carving face. On the other hand, if the rider 3 is travelling too slowly for a particular carving face then the centrifugal force acting on the rider 3 will be insufficient to balance the weight of the rider 3 as he leans over. In this case, the snow deck 1 will cause the lean of the rider 3 to be increased so that he uses a less central carving edge, and thus balancing the velocity, radius of turn and lean of the rider 3.

[0072] Once the intended velocities have been chosen for the carving faces, their tilt angles can be chosen. The tilt angles should be chosen so that the carving faces are sufficiently spaced around the hull in order that the carving faces (together with their associated running faces and recess faces) do not interfere with each other. For example, tilt angles of 2°, 4° and 6° would not give satisfactory results in most circumstances as the carving edges would be crowded around a small region of the hull. The maximum tilt angle depends on the width of the snow deck 1 and on the height of the deck 11 above the footprint of the hull 9. A wider, higher snowdeck will allow the rider 3 to attain greater angles of tilt.

[0073] For the snowdeck 1, the angles 11°, 18.4° and 30° have been selected for the carving faces 21, 23, 25 respectively. Equation (1) gives the radii 4.7 m, 1.9 m and 0.7 m, respectively. Most pistes are inclined at an angle of about 15° which is sufficiently small that the cos(slope) term can be ignored in most cases when calculating the curvature of the carving faces.

[0074] The height of the carving faces 21, 23, 25 has been set to 15 mm in this embodiment of the snowdeck 1. This value was chosen with regard to the transverse profile of the recess faces 41, 43, 45 to ensure that the height of the carving faces 21, 23, 25 provides sufficient lateral grip on the snow 5, and to ensure that the transverse profile of the hull 9 is such that the hull 9 does not sink too deeply into the snow 5. If the hull were to sink excessively into the snow then the entire underside of the hull would be in contact with the snow 5, causing friction to increase to excessive levels.

[0075]FIG. 11 shows a hull 111 which may be attached to the deck of a conventional skateboard to form a snowdeck. The underside of the hull 111 has the same shape as the hull 9 so that the hull 111 can also be used to produce carving turns. Ribs and stiffeners 112 increase the rigidity of the hull 111 and also allow the weight of a rider 3 to be transferred from the skateboard (not shown) to the hull 111.

[0076] The wheels of a skateboard are generally mounted on mountings known as “trucks” and each of the two trucks is mounted at one end of a skateboard deck. Each truck is typically secured using four bolts which pass through the skateboard deck and into the truck.

[0077] The hull 111 is provided with mounting holes 113 at one end and with slots 114 at the other end so that the hull 111 can be readily attached to a conventional skateboard deck. The mounting holes 113 are spaced so that they conform to the standard pattern of mounting holes used to secure a truck to a skateboard deck. However, the lengths of skateboards are typically in the range 76 cm (30 inches) to 86 cm (34 inches) and have their sets of truck fixing holes spaced apart by different lengths. It is desirable that the hull 111 should be attachable to skateboard decks of different lengths in this range. The slots 114 allow mounting bolts, for example self tapping screws, to be inserted anywhere along the length of the slots 114, thus enabling the hull 111 to be secured to a skateboard having lengths in a predetermined range. Skateboards of different lengths have different distances between their sets of truck mounting holes and so the slots 114 accommodate these different distances. The hull 11 is preferably formed from polyethylene which may be injection moulded around a foam core or rotationally moulded. An elastomeric mounting gasket (not shown) is preferably used to seal the hull 111 to the underside of the skateboard deck, in order to prevent the ingress of snow.

[0078] The hull 111 may also be adapted to be fixed to either the wheels or the axles of a skateboard in order to convert the skateboard into a snowdeck. The hull will in this alternative be provided with attachment portions for fixing to the skateboard wheels or axles, preferably without the use of tools.

[0079]FIG. 12a shows a rider riding on a carving toboggan 120. The rider 3 is shown sitting on a platform 121 which is attached to a plurality of runners 122. The runners 122 are similar to the carving faces 21, 23, 25 and running edges 31, 33, 35 of the snowdeck 1 but combine the functionality of a carving face, a running face and a recess face. The runners 122 are attached to the platform 121 by means of a space frame 123. In contrast to the snowdeck 1, the surface area and displacement of the runners 122 is such that a hull is not required to prevent the runners 122 from sinking excessively into snow.

[0080] The centre of gravity of the rider 3 is relatively low because the rider 3 is sitting down on the platform 121. This enables the rider 3 to use greater angles of tilt than are possible on a snowdeck. For example, runners 122 may be provided for use at a tilt angle of 55° off vertical. The carving toboggan 120 is longer than a typical snowdeck and this, together with the fact that the rider 3 is sitting down, allows the carving toboggan 120 to be used on steeper pistes and thus at higher speeds than the snowdeck. The higher speeds and the greater angles of tilt are reflected in the curvature of the runners 122.

[0081]FIG. 12b shows a carving toboggan 125 that may be used by a rider 3 either sitting down or standing up. Foot straps 126 are provided to secure the rider 3 to the carving toboggan 125 when he is standing up.

[0082]FIG. 13 shows an ice skating boot 130 which is provided with a straight blade 131 for travelling in a straight line and with carving blades 132 for performing turns. Whereas the hull 9 of the snowdeck 1 was shaped to minimise the extent to which the hull 9 sank into snow 5, ice is much harder than snow and therefore the blades 131, 132 will not sink appreciably into ice. The correspondence between the curvature of the carving blades 132 and their angle of tilt is similar to that described for embodiment 1 except that the speeds achievable on ice are significantly faster which is reflected in the radii of the carving blades 132.

[0083] Further Embodiments

[0084] The hull 9 was described as having an arcuate transverse profile near to the end regions 27 and consequently had a flatter profile at the centre of the hull 9. In an alternative embodiment, a hull may be designed to have an arcuate transverse profile in the centre with the result that it will have a more pronounced (i.e more sharply curved than at the centre, and thus resembling a canoe more than the hull 9 of the first embodiment) transverse profile at the ends of the hull. This embodiment may be preferred in some circumstances but in general is not preferred as it will tend to dig into snow (rather than planing on top of the snow), thus suffering increased friction.

[0085] The hull 9 was earlier described as having a generally arcuate profile towards the end regions 27, and a flatter profile at the centre of the hull 9. In an alternative embodiment the hull need not have an arcuate profile that is part of a circle but may instead have a profile that is curved in some other way, for example an elliptical profile. Whatever shape is chosen, a relatively flat profile will tend to be more stable and suitable for beginners whereas a relatively sharply curved profile will offer greater performance to experienced riders.

[0086] The hull 9 had carving faces 21, 23, 25 which were designed for use at different speeds. In an alternative embodiment, a hull is provided with carving faces which are designed for use at a common speed. Such a hull may be preferred for use on “slalom” type pistes, where a rider will typically wish to execute carving turns of different radii at a relatively constant forward velocity.

[0087] The hull 9 was earlier described as being symmetric about the longitudinal axis 15. In an alternative embodiment, a hull has carving edges on one side that are different from those on the other side. The carving edges may be designed for different angles of tilt, different speeds or for both different angles of tilt and different speeds. Such a hull could be produced in left and right handed versions to suit the riding style of riders. By analogy, snowboards can be ridden in a conventional right handed way (known as “regular” in which the rider's left shoulder leads down the slope) or in a left handed way (known as “goofy”).

[0088] The two ends of the hull 9 were described earlier as being symmetric about the transverse axis 17. In an alternative embodiment, the tilt, and angle of curvature, of the carving faces is different at the two opposite ends of the hull. This embodiment could be used to provide a snowdeck suitable for both beginners and more advanced riders. Beginners would place their centre of gravity over the “low speed” end of the board to use the region of the carving faces having tilts and curvatures more suitable for beginners. More advanced riders would place their centre of gravity over the “high speed” end of the hull to use the region of the carving faces having tilts and curvatures more appropriate to advanced riders. Another benefit of the embodiment is that it would allow slalom riders (who will generally travel at a rapid and relatively constant speed) to change the radius of a turn (whilst travelling at a constant speed) by moving their centre of gravity forwards or backwards relative to the deck). In such an embodiment the set of carving faces at each end of the hull have their own respective radii and tilts. In the region of the centre of the hull, the two sets of carving faces join up and undergo a smooth transition between the radii and tilts used at the opposite ends. Thus, in such an embodiment, the carving edges are no longer parts of a single cylinder but are a combination of parts of two different cylinders with a transition region between the two different ends.

[0089] The hull 9 described above had a single straight surface 19 and three carving edges 21, 23, 25 on each side of the surface 19. In alternative embodiments a smaller or greater number of carving edges may be used on each side of the longitudinal axis 15. In an alternative embodiment, a single carving edge is provided on each side of the longitudinal axis 15. In yet further embodiments, a “left hand turn only” hull is provided which has a single straight surface and one (or more) carving edges (located on the same side of the surface 19) for performing turns. These embodiments can make carving right handed turns only when the direction of the board is reversed by the rider executing a 180° rotation of the board.

[0090] The hull 9 had a single straight surface 19 which was relatively wide. In an alternative embodiment the straight surface 19 may be replaced by two carving and running faces, the two carving faces being straight and parallel. Alternatively, the two carving faces may be slightly curved, one for performing very gentle turns to the left and the other for performing very gentle turns to the right. In such an embodiment, when the hull is travelling in a straight line these two central gently carving faces will to some extent conflict with each other which may increase the friction. However, the provision of these two gently carving faces may allow for improved high speed control in some embodiments.

[0091] The hull 9 was described as having integrally formed carving faces and running faces. In an alternative embodiment the carving faces and running faces are replaceable to allow for their renewal if they become excessively worn or so that the material of the carving faces and running faces can be selected to give optimum performance for the snow (for example whether the snow is powdery or compacted). In some circumstances it may also be desirable to be able to replace the recess faces, for example to change the footprint of the hull and hence the depth to which it sinks in snow. The carving, running or recess faces could be replaced either by securing a piece of material to the faces or by using replaceable runners which would be attached to the hull rather than being integrally formed with the hull. A replaceable runner would typically comprise a carving face, a running face and a recess face. The use of replacement runners would also allow beginners to upgrade the profile of the runners, and thereby modify the tilt and curvature to some extent, as their skill level increases. The use of replacement runners would also allow a hull to be used on a highly abrasive medium such as sand.

[0092] The running faces 31, 33, 35 were earlier described as joining the carving faces 21, 23, 25 at right angles. In alternative embodiments this angle may be less than or greater than 90°. In yet further embodiments, the running faces may be dispensed with so that the recess faces meet their respective carving faces at an acute angle. Although this yet further embodiment simplifies the profile of the carving faces and recess faces, the edges where the carving faces and running faces join may be excessively prone to breakage and so they may need to be manufactured from a strong material such as a metal, for example steel.

[0093] The recess faces 41, 43, 45 were shown in FIGS. 6 and 7 as forming a straight line between their respective carving faces and running faces. In alternative embodiments the recess faces may be curved in transverse profile. This curvature may be advantageously used to control the extent to which a hull sinks into snow. Similarly, the carving faces and the running faces may also be curved in the planes XX′ and YY′ visible in FIGS. 6 and 7 although it is preferred that they are straight. The carving faces, running faces and recess faces may be combined into other shapes, for example into a semi-circular shape in transverse profile. What is important is that the runner, whatever shape is used, is able to support the weight of the rider and is able to exert a reaction force to oppose the centrifugal and body forces exerted on the rider.

[0094] The hull 9 was described as being formed from polyethylene. Other materials such as polypropylene, other plastics, woods or metals are also suitable although a factor to be borne in mind when selecting a plastic is that it must not be excessively brittle at low temperatures. Nylon is not preferred as it tends to have excessive friction on snow. The blades 131, 132 of the ice skating boot 130 or those of the carving toboggan 120 may be conveniently formed from a metal, for example stainless steel, or even wood.

[0095] When a pair of ice skating boots 130 are used as a pair, the blades 131, 132 on each boot will typically be identical so that the only differences between the left and the right boots will be so that they fit a left foot and a right foot, respectively. In an alternative embodiment, the blades 131, 132 of a pair of ice skates are shaped so that they are mirror images of each other. This allows for improved turning ability. For example, consider a situation where an ice skater is following a circular path to the right. The skate on the right foot will follow a circular path having a slightly smaller radius than the circular path followed by the skate on the left foot. Consequently, in this alternative embodiment, the carving blades 132 on the right hand side of the right foot are provided with a slightly smaller radius of curvature than the carving blades 132 on the right hand side of the left boot.

[0096] Carving toboggans were shown in relation to FIGS. 12a and 12 b. In an alternative embodiment, the runners 122 of the carving toboggans are narrowed so that they become blades, thus providing a carving bobsleigh for use on bobsleigh tracks.

[0097] In another embodiment, a modified carving toboggan is fitted for use as the front ski of a skidoo or snowmobile, thereby improving the steerability of the skidoo or snowmobile to which it is fitted. Such a modified carving toboggan may be provided with mounting fixtures so that it can be used to replace and thereby upgrade the front skis of the skidoo or snowmobile.

[0098] “Inline” skates are well known for use on, for example, grass or concrete and comprise several small wheels mounted one behind the other and having parallel axes. Whereas the previous embodiments were suitable for use on media such as snow, sand and ice, in an alternative embodiment inline wheels are used so that the alternative embodiment can be made to turn on, for example, grass or concrete by tilting it appropriately. In this alternative embodiment the straight surface 19 is replaced by inline wheels and the carving edges 21, 23, 25 and their associated running edges 31, 33, 35 are replaced by wheels which rather than being in line are angled so that their axes are tangential to a circular arc. As before, these circular arcs are tilted so that the user of this alternative embodiment can make a turn by tilting the embodiment so that the inline wheels are lifted off the ground and the apparatus is instead supported by a set of wheels arranged around an arc. 

1. A hull (1, 9, 111) for sliding over a carveable medium (5), and having a longitudinal axis (15) about which the hull can roll relative to the medium, the hull comprising: straight runner means (19) for travelling on the medium in a substantially straight line (90 a) when the hull is at a first roll angle relative to the medium; and a longitudinally extending curved runner (21, 31, 43; 23, 33, 45; 25, 35, 47) convex towards the straight runner means and arranged to contact the medium when the hull is at a second roll angle (b, c, d) relative to the medium; characterised in that the curved runner comprises a substantially circularly arcuate portion (21, 23, 25) of a first radius (r1, r2, r3) for travelling on the medium in a substantially circular path (90 b, 90 c, 90 d) by carving the medium when the hull is at the second roll angle, and in that relative to the longitudinal axis, the straight runner means and the curved runner comprise a portion towards the middle (FIG. 7) and two end portions (FIG. 6), and wherein the straight runner means and the curved runner are arranged in a first arc (51X), when viewed at an end portion in a plane (XX′) transverse to the longitudinal axis, and in a second arc (51Y), when viewed at the middle portion in a plane (YY′) transverse to the longitudinal axis, and wherein the first arc is more tightly curved than the second arc.
 2. A hull according to claim 1, wherein the straight runner means (19) comprises a straight surface (19).
 3. A hull according to claim 1, wherein the straight runner means (19) comprises a pair of oppositely curved runners convex towards each other.
 4. A hull according to any of claims 1 to 3, wherein the curved runner is a first curved runner, the hull further comprising a second longitudinally extending curved runner arranged on the side of the straight runner means (19) opposite to the first curved runner and convex toward the straight runner means, wherein the second curved runner comprises a substantially circularly arcuate portion (21, 23, 25) of a second radius (r1, r2, r3) for travelling on the medium (5) in a substantially circular path (90 b, 90 c, 90 d) by carving the medium (5) when the vehicle is at a third roll angle (b, c, d) relative to the medium.
 5. A hull according to claim 4, wherein the first and second radii are equal.
 6. A hull according to claim 5, wherein the first and second curved runners are symmetrically arranged with respect to the straight runner means (19).
 7. A hull according to claim 4, 5 or 6, comprising a plurality of longitudinally extending curved runners arranged on one side of the straight runner means (19), each curved runner being convex toward the straight runner means and comprising a respective substantially circularly arcuate portion (21, 23, 25) of a respective radius (r1, r2, r3) for travelling on the medium (5) in a substantially circular path of that radius (90 b, 90 c, 90 d) by carving the medium when the vehicle is at a respective roll angle (b, c, d) relative to the medium.
 8. A hull according to claim 7, wherein the respective roll angle (b, c, d) of a curved runner nearer the straight runner means (19) is less than the roll angle of a curved runner spaced further from the straight runner means.
 9. A hull according to claim 4, 5 or 6, comprising a plurality of longitudinally extending curved runners arranged on each side of the straight runner means (19), each curved runner being convex toward the straight runner means and comprising a respective substantially circularly arcuate portion (21, 23, 25) of a respective radius (r1, r2, r3) for travelling on the medium (5) in a substantially circular path of that radius (90 b, 90 c, 90 d) by carving the medium when the vehicle is at a respective roll angle (b, c, d) relative to the medium.
 10. A hull according to claim 9, wherein the curved runners are symmetrically arranged with respect to the straight runner means (19).
 11. A hull according to any one of claims 4, 5, 7 to 10, wherein each of the circularly arcuate portions (21, 23, 25) has a tilt-radius product defined by the tangent of the roll angle (b, c, d) associated with the circularly arcuate portion multiplied by the radius (r1, r2, r3) associated with the circularly arcuate portion, and wherein the tilt-radius products of the circularly arcuate portions are substantially equal.
 12. A hull according to any one of claims 4, 5, 7 to 10, wherein each of the circularly arcuate portions (21, 23, 25) has a tilt-radius product defined by the tangent of the roll angle (b, c, d) associated with the circularly arcuate portion multiplied by the radius (r1, r2, r3) associated with the circularly arcuate portion, and wherein for any two circularly arcuate portions having different associated roll angles, the tilt-radius product of the circularly arcuate portion having the smaller associated roll angle is larger than the tilt-radius product of the circularly arcuate portion having the larger associated roll angle.
 13. A hull according to claim 12 when dependent on any one of claims 7 to 10, comprising three circularly arcuate portions (21, 23, 25) arranged on a side of the straight runner means (19), wherein the tilt-radius products of the three circularly arcuate portions are substantially in the ratio 9:6:3.
 14. A hull according to claim 13, wherein the tilt-radius products of the three circularly arcuate portions (21, 23, 25) are substantially 0.9, 0.6 and 0.4 when their associated radii (r1, r2, r3) are measured in metres.
 15. A hull according to any preceding claim, wherein the curved runner or runners comprise first and second circularly arcuate portions having different centres of curvature.
 16. A hull according to any preceding claim, wherein, relative to the longitudinal axis (15), the straight runner means (19) and the one or more curved runners comprise a portion towards the middle (FIG. 7) and two end portions (FIG. 6), and wherein the straight runner means and the one or more curved runners are arranged in a substantially circular arc (51X) when viewed at an end portion in a plane (XX′) transverse to the longitudinal axis.
 17. A hull according to any preceding claim, wherein the circularly arcuate portion of the curved runner or runners comprises a cylindrical carving face (21, 23, 25).
 18. A hull according to claim 17, wherein the circularly arcuate portion of the curved runner or runners comprises a circularly arcuate running face (31, 33, 35) which meets the carving face (21, 23, 25) at an edge.
 19. A hull according to claim 18, wherein the running face meets the carving face at an angle of from 75° to 105°.
 20. A hull according to claim 19, wherein the running face meets the carving face at an angle of 90°.
 21. A vehicle comprising a hull according to any preceding claim and a deck (11), wherein the deck is mounted on the hull and the hull is integrally formed with the straight runner means (19) and the one or more curved runners.
 22. A vehicle according to claim 21, wherein the hull (9) comprises a substantially cylindrical central portion and a pair of upwardly inclined tapered ends (27).
 23. A vehicle according to claim 22, wherein the tapered ends (27) are upwardly inclined at an angle (α) in the range 30° to 45°.
 24. A vehicle according to claim 23, wherein the tapered ends (27) are upwardly inclined at an angle (α) of 38°.
 25. A vehicle according to any preceding claim, wherein at least a portion of the straight runner means (19) or the one or more curved runners is replaceable.
 26. A vehicle according to any preceding claim, further comprising an attachment point (2) for a leash (4).
 27. A hull (9) for a vehicle according to any one of claims 21 to
 26. 28. A hull according to claim 27, wherein the hull is formed from a moulded plastics material.
 29. A hull according to claim 27 or 28, for fixing to a deck (11), the hull comprising two mounting regions (113, 114) for attaching the hull to the deck by means of fasteners (14) passing through the deck.
 30. A hull according to claim 29, wherein one of the mounting regions comprises a plurality of mounting holes (113) and the other mounting region comprises a pair of slots (114) extending longitudinally of the hull.
 31. A hull according to claim 27 or claim 28, further comprising attachment means for attaching the hull to a skateboard.
 32. A hull according to claim 31, wherein the hull is attachable to a skateboard by engaging the skateboard wheels.
 33. A hull according to claim 31, wherein the hull is attachable to a skateboard by engaging the skateboard axles.
 34. A vehicle (1; 9; 111; 129; 130) for sliding over a carveable medium (5) and having a longitudinal axis (15) about which the vehicle can roll relative to the medium, the vehicle comprising: straight runner means (19) for travelling on the medium in a substantially straight line (90 a) when the vehicle is at a first roll angle relative to the medium; and a longitudinally extending curved runner (21, 31, 43; 23, 33, 45; 25, 35, 47) convex towards the straight runner means and arranged to contact the medium when the vehicle is at a second roll angle (b, c, d) relative to the medium; characterised in that the curved runner is substantially part of a surface of revolution of a first radius (r1, r2, r3) about an axis that i) lies in a plane perpendicular to the said longitudinal axis, ii) is positioned towards the middle of the vehicle and iii) is inclined so that the curved runner can carve a substantially circular path (90 c, 90 c, 90 d) in the medium when the vehicle is at the second roll angle.
 35. A vehicle according to claim 34, wherein the straight runner means (19) comprises a straight surface (19).
 36. A vehicle according to claim 34, wherein the straight runner means (19) comprises a pair of oppositely curved runners convex towards each other.
 37. A vehicle according to any one of claims 34 to 36, wherein the curved runner is a first curved runner and further comprising a second longitudinally extending curved runner arranged on the side of the straight runner means (19) opposite to the first curved runner and convex toward the straight runner means and arranged to contact the medium (5) when the vehicle is at a third roll angle (b, c, d,) relative to the medium, and wherein the second curved runner is substantially part of a surface of revolution of a second radius (r1, r2, r3) about an axis that i) lies in a plane perpendicular to the longitudinal axis, ii) is positioned towards the middle of the vehicle and iii) is inclined so that the curved runner can carve-a substantially circular path (90 b, 90 c, 90 d) in the medium when the vehicle is at the third roll angle.
 38. A vehicle according to claim 37, wherein the first and second radii are equal.
 39. A vehicle according to claim 38, wherein the first and second curved runners are symmetrically arranged with respect to the straight runner means (19).
 40. A vehicle according to claim 37, 38 or 39, comprising a plurality of longitudinally extending curved runners arranged on one side of the straight runner means (19), each curved runner being convex toward the straight runner means and arranged to contact the medium (5) when the vehicle is at a respective roll angle (b, c, d) relative to the medium, wherein each curved runner is substantially part of a respective surface of revolution of a respective radius (r1, r2, r3) about a respective axis that i) lies in a plane perpendicular to the longitudinal axis, ii) is positioned towards the middle of the vehicle and iii) is inclined so that each curved runner can carve a respective substantially circular path (90 b, 90 c, 90 d) in the medium when the vehicle is at the respective roll angle.
 41. A vehicle according to claim 40, wherein the respective roll angle (b, c, d) of a curved runner nearer the straight runner means (19) is less than the roll angle of a curved runner spaced further from the straight runner means.
 42. A vehicle according to claim 37, 38 or 39, comprising 1 a plurality of longitudinally extending curved runners arranged on each side of the straight runner means (19), each curved runner being convex toward the straight runner means and arranged to contact the medium (5) when the vehicle is at a respective roll angle (b, c, d) relative to the medium, wherein each curved runner is substantially part of a respective surface of revolution of a respective radius (r1, r2, r3) about a respective axis that lies i) in a plane perpendicular to the longitudinal axis (15), ii) is positioned towards the middle of the vehicle and iii) is inclined so that each curved runner can carve a respective substantially circular path (90 b, 90 c, 90 d) in the medium when the vehicle is at the respective roll angle.
 43. A vehicle according to claim 42, wherein the curved runners are symmetrically arranged with respect to the straight runner means (19).
 44. A vehicle according to any one of claims 37, 38, 40 to 43, wherein each of the curved runners has a tilt-radius product defined by the tangent of the roll angle (b, c, d) associated with the curved runner multiplied by the radius (r1, r2, r3) associated with the curved runner, and wherein the tilt-radius products of the curved runners are substantially equal.
 45. A vehicle according to any one of claims 37, 38, 40 to 43, wherein each of the curved runners has a tilt-radius product defined by the tangent of the roll angle (b, c, d) associated with the curved runner multiplied by the radius (r1, r2, r3) associated with the curved runner, and wherein for any two curved runners having different associated roll angles, the tilt-radius product of the curved runner having the smaller associated roll angle is larger than the tilt-radius product of the curved runner having the larger associated roll angle.
 46. A vehicle according to claim 45 when dependent on any one of claims 40 to 43, comprising three curved runners arranged on a side of the straight runner means (19), wherein the tilt-radius products of the three curved runners are substantially in the ratio 9:6:3.
 47. A vehicle according to claim 46, wherein the tilt-radius products of the three curved runners are substantially 0.9, 0.6 and 0.4 when their associated radii (r1, r2, r3) are measured in metres.
 48. A vehicle according to any one of claims 34 to 47, wherein the curved runner or runners comprise first and second surfaces of revolution, about different axes.
 49. A hull according to any one of claims 34 to 48, wherein, relative to the longitudinal axis (15), the straight runner means (19) and the one or more curved runner comprise a portion towards the middle (FIG. 7) and two end portions (FIG. 6), and wherein the straight runner means and the one or more curved runners are arranged in a first arc (51X), when viewed at an end portion in a plane (XX′) transverse to the longitudinal axis, and in a second arc (51Y), when viewed at the middle portion in a plane (YY′) transverse to the longitudinal axis, and wherein the first arc is more tightly curved than the second arc.
 50. A vehicle according to any one of claims 34 to 49, wherein, relative to the longitudinal axis (15), the straight runner means (19) and the one or more curved runners comprise a portion towards the middle (FIG. 7) and two end portions (FIG. 6), and wherein the straight runner means and the one or more curved runners are arranged in a substantially circular arc (51X) when viewed at an end portion in a plane (XX′) transverse to the longitudinal axis.
 51. A vehicle according to any one of claims 34 to 50, wherein the circularly arcuate portion of the curved runner or runners comprises a cylindrical carving face (21, 23, 25).
 52. A vehicle according to claim 51, wherein the circularly arcuate portion of the curved runner or runners comprises a circularly arcuate running face (31, 33, 35) which meets the carving face (21, 23, 25) at an edge.
 53. A vehicle according to claim 52, wherein the running face meets the carving face at an angle of from 75° to 105°.
 54. A vehicle according to claim 53, wherein the running face meets the carving face at an angle of 90°.
 55. A vehicle according to any one of claims 34 to 54, comprising a deck (11) and a hull (9), wherein the deck is mounted on the hull and the hull is integrally formed with the straight runner means (19) and the one or more carved runners.
 56. A vehicle according to claim 55, wherein the hull (9) comprises a substantially cylindrical central portion and a pair of upwardly inclined tapered ends (27).
 57. A vehicle according to claim 56, wherein the tapered ends (27) are upwardly inclined at an angle (α) in the range 30° to 45°.
 58. A vehicle according to claim 57, wherein the tapered ends (27) are upwardly inclined at an angle (α) of 38°.
 59. A vehicle according to any one of claims 34 to 58, wherein at least a portion of the straight runner means (19) or the one or more curved runners is replaceable.
 60. A vehicle according to any one of claims 34 to 59, further-comprising an attachment point (2) for a leash (4).
 61. A hull (9) for a vehicle according to any one of claims 55 to
 60. 62. A hull according to claim 61, wherein the hull is formed from a moulded plastics material.
 63. A hull according to claim 61 or 62, for fixing to a deck (11), the hull comprising two mounting regions (113, 114) for attaching the hull to the deck by means of fasteners (14) passing through the deck.
 64. A hull according to claim 63, wherein one of the mounting regions comprises a plurality of mounting holes (113) and the other mounting region comprises a pair of slots (114) extending longitudinally of the hull.
 65. A hull according to claim 61 or claim 62, further comprising attachment means for attaching the hull to a skateboard.
 66. A hull according to claim 65, wherein the hull is attachable to a skateboard by engaging the skateboard wheels.
 67. A hull according to claim 65, wherein the hull is attachable to a skateboard by engaging the skateboard axles.
 68. A vehicle according to any one of claims 34 to 54, wherein the straight runner means (19) is attached to the one or more curved runners by a space frame (123).
 69. A vehicle according to any one of claims 34 to 54, or 68, adapted for use as a toboggan (120; 125).
 70. A vehicle according to any one of claims 34 to 54 or 68, adapted for use as an ice skating boot (130).
 71. A pair of vehicles according to claim 70, wherein the curvatures of the curved runners are arranged such that the curved runners of the two vehicles carve circles of different respective radii on the ice when the boots are inclined at the same roll angle.
 72. A vehicle according to any one of claims 34 to 54, or 68, adapted for use as a ski for a snowmobile.
 73. A vehicle for travelling over a surface, and having a longitudinal axis about which the vehicle can roll relative to the surface, the vehicle comprising: straight runner means comprising a row of wheels for travelling on the surface in a substantially straight line when the vehicle is at a first roll angle relative to the surface; and two or more curved runners convex toward the straight runner means and each comprising an arcuate row of wheels arranged in an arc of substantially circular shape of a respective radius for travelling on the surface in a substantially circular path when the vehicle is at a respective roll angle relative to the surface, characterised in that each of the curved runners has a tilt-radius product defined by the tangent of the roll angle associated with the curved runner multiplied by the radius associated with the curved runner, and wherein the tilt-radius products of the curved runners are substantially equal.
 74. A vehicle for travelling over a surface, and having a longitudinal axis about which the vehicle can roll relative to the surface, the vehicle comprising: straight runner means comprising a row of wheels for travelling on the surface in a substantially straight line when the vehicle is at a first roll angle relative to the surface; and two or more curved runners convex toward the straight runner means and each comprising an arcuate row of wheels arranged in an arc of substantially circular shape of a respective radius for travelling on the surface in a substantially circular path when the vehicle is at a respective roll angle relative to the surface, characterised in that each of the curved runners has a tilt-radius product defined by the tangent of the roll angle associated with the curved runner multiplied by the radius associated with the curved runner, and wherein for any two curved runners having different associated roll angles, the tilt-radius product of the curved runner having the smaller associated roll angle is larger than the tilt-radius product of the curved runner having the larger associated roll angle. 